We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a sphere with at least 5 punctures. In particular, we show that any injective homomorphism between these groups is given by a homeomorphism of a punctured sphere together with a map to the integers. The technique, following Ivanov, is to prove that every superinjective map of the curve complex of a sphere with at least 5 punctures is induced by a homeomorphism. We also determine the automorphism group of the pure braid group on at least 4 strands.
Cite this article
Robert Bell, Dan Margalit, Injections of Artin groups. Comment. Math. Helv. 82 (2007), no. 4, pp. 725–751DOI 10.4171/CMH/108